Why were merchants in the cottage industry trying to avoid dealing with guilds in the cities

Because Guilds in the cities were considered controversial.

Explanation:

During medieval era, Guilds in the cities were creating monopolies in the industry, and were creating restrictions to the quantity or availability of craftsmen in certain craft, there by limiting or taking out competition and free market.

Hence, cottage industry outside the cities are avoiding to do business with them due to their controversial nature.

b. the passage of the equal rights amendment  

explanation:

this mean that anything that someone else could do they could do